Method and system for correcting chromatic aberrations of a color image produced by an optical system

ABSTRACT

A system and a method for correcting chromatic aberrations of a color image composed of a plurality of digitized color planes. The color image is assumed to have been produced by an optical system. According to the system and method, geometric anomalies of the digitized color planes are modeled and corrected, at least partly, in such a way to obtain corrected digitized color planes. The corrected digitized color planes are then combined to obtain a color image corrected completely or partly for the chromatic aberrations. The system and method are applicable to photographic or video image processing, in optical devices, industrial controls, robotics, metrology, etc.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to a method and a system for correctingthe chromatic aberrations of a color image produced by means of anoptical system.

BRIEF SUMMARY OF THE INVENTION Method

The invention relates to a method for correcting the chromaticaberrations of a color image composed of a plurality of digitized colorplanes. The color image was produced by means of an optical system. Themethod includes the following stages:

-   -   the stage of modeling and correcting, at least partly, the        geometric anomalies of the digitized color planes, in such a way        as to obtain corrected digitized color planes,    -   the stage of combining the corrected digitized color planes, in        such a way as to obtain a color image corrected completely or        partly for the chromatic aberrations.

Preferably, according to the invention, the method includes the stage ofmodeling and correcting, at least partly, the geometric anomaliescomposed of deviations between the geometric defects, especiallydistortion, of the digitized color planes, in such a way as to obtaincorrected digitized color planes. Thus it is possible to establish acorrespondence between the corrected digitized color planes. The methodadditionally includes the stage of combining the corrected digitizedcolor planes in such a way as to obtain a color image correctedcompletely or partly for the chromatic aberrations.

Preferably, according to the invention, the method includes the stage ofmodeling and correcting, at least partly, the geometric anomaliescomposed of distortion defects of the digitized color planes, in such away as to obtain corrected digitized color planes. Thus it is possibleto establish a correspondence between the corrected digitized colorplanes. The method additionally includes the stage of combining thecorrected digitized color planes in such a way as to obtain a colorimage corrected completely or partly for the chromatic aberrations andthe distortion defects.

System

The invention also relates to a system for correcting the chromaticaberrations of a color image composed of a plurality of digitized colorplanes. The color image was produced by means of an optical device. Thesystem comprises:

-   -   first calculating means for modeling and correcting the        geometric anomalies of the digitized color planes, in such a way        as to obtain corrected digitized color planes,    -   second calculating means for combining the corrected digitized        color planes, in such a way as to obtain a color image corrected        completely or partly for the chromatic aberrations.

Preferably, according to the invention, the system includes firstcalculating means for modeling and correcting, at least partly, thegeometric anomalies composed of deviations between the geometricdefects, especially distortion, of the digitized color planes, in such away as to obtain corrected digitized color planes. Thus it is possibleto establish a correspondence between the corrected digitized colorplanes. The system additionally includes second calculating means forcombining the corrected digitized color planes in such a way as toobtain a color image corrected completely or partly for the chromaticaberrations.

Preferably, according to the invention, the color image was produced bymeans of an optical device system. The system includes first calculatingmeans for modeling and correcting, at least partly, the geometricanomalies composed of distortion defects of the digitized color planes,in such a way as to obtain corrected digitized color planes. Thus it ispossible to establish a correspondence between the corrected digitizedcolor planes. The system additionally includes second calculating meansfor combining the corrected digitized color planes in such a way as toobtain a color image corrected completely or partly for the chromaticaberrations and the distortion defects.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Other characteristics and advantages of the invention will becomeapparent upon reading of the description of alternative embodiments ofthe invention, provided by way of indicative and non-limitativeexamples, and of

FIG. 1, which illustrates a first alternative embodiment of a systemaccording to the invention, designed more particularly to correct thechromatic aberrations and the distortion defects,

FIG. 2, which illustrates a second alternative embodiment of a systemaccording to the invention, designed more particularly to correct thechromatic aberrations,

FIGS. 3 to 7, which illustrate a third alternative embodiment of asystem according to the invention, designed more particularly to correctthe chromatic aberrations and the distortion defects,

FIG. 8, which illustrates a practical example of a system according tothe invention,

FIG. 9, which illustrates a second practical example of a systemaccording to the invention.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIG. 1, a description will now be given of the firstalternative embodiment.

In the case of the first alternative embodiment, the system is designedmore particularly to correct the chromatic aberrations 1 and thedistortion defects 2 of a color image 3 composed of a plurality ofdigitized color planes 4. Color image 3 was produced by means of anoptical system 5.

The system includes first calculating means 6 for modeling andcorrecting, at least partly, the distortion defects 2 of digitized colorplanes 4, in such a way as to obtain corrected digitized color planes 7.Thus it is possible to establish a correspondence 20 between correcteddigitized color planes 7.

The system additionally includes second calculating means 8 forcombining corrected digitized color planes 7, in such a way as to obtaina color image 9 corrected completely or partly for the chromaticaberrations 1 and the distortion defects 2.

Referring to FIG. 2, a description will now be given of the secondalternative embodiment.

In the case of the second alternative embodiment, the system is designedmore particularly to correct the chromatic aberrations. As in the caseof the first alternative embodiment, color image 3 was produced by meansof an optical system 5. The system includes first calculating means 16for modeling and correcting, at least partly, the deviations 10 betweenthe distortion defects 2 of digitized color planes 4, in such a way asto obtain corrected digitized color planes 17. Thus it is possible toestablish a correspondence 21 between corrected digitized color planes17.

The system additionally includes second calculating means 18 forcombining the corrected digitized color planes 17, in such a way as toobtain a color image 19 corrected completely or partly for the chromaticaberrations 1.

In the case of a third alternative embodiment, the system is moreparticularly designed to correct the chromatic aberrations of a colorimage composed of digitized color planes. We will present a detailedexplanation of a practical example that includes the stage of modelingand correcting the geometric anomalies, such as distortion, of thedigitized color planes, in such a way as to obtain corrected digitizedcolor planes, and the stage of combining the corrected digitized colorplanes, in order to obtain a color image corrected for the chromaticaberrations. The color image is produced by means of an optical systemwhich, in the described example, comprises capturing or restituting thecolor image by means of an appliance and/or of an appliance chain.

Modeling

FIG. 3 illustrates a precise description of an example of implementationof the system of the invention and of the method employed. First of allwe shall attempt to describe an example of a modeling process dedicatedexclusively to the distortion defects of image I that correspond to onedigitized color plane. The approach will then be applied to colorimages, then permitting modeling and correction of chromatic and/orgeometric aberrations. The process described in FIG. 3 employs:

-   -   a universal set M, which may be a reference scene,    -   a medium SC containing an image I. In the case of an        image-capture system, surface SC may be that of a sensor (such        as a CCD) or, in the case of an image-restitution system, this        surface may be that of a projection screen or that of a paper        sheet of a printer.    -   a virtual reference surface SR containing a virtual reference R        or a virtual reference image, which if necessary may be a        synthetic image.

By means of an appliance APP1 or of an appliance chain, image I isobtained, from universal set M, on a medium SC, keeping only onedigitized color plane. An appliance chain is a set of appliances withwhich an image can be obtained. For example, an appliance chainApp1/App2/App3 will be able to include an image-capture appliance, ascanner, a printing appliance, etc.

Image I therefore contains defects and, in particular, distortiondefects related to these appliances.

Virtual reference R is deduced directly from M, and must be regarded asperfect or quasi-perfect. It may be identical or quasi-identical to M,or instead may exhibit differences, as will be seen farther on.

As an example, we can explain the relationship between M and R asfollows: To points PP1 to PPm of universal set M there correspondreference points PR1 to PRm in virtual reference R of reference surfaceSR as well as characteristic image points PT1 to PTm of image I ofmedium SC.

According to a practical example of the method of the invention, thereis therefore provided a stage of modelling of defects from image I,which has been captured and/or restituted by means of the appliance orof appliance chain APP1.

In the course of a subsequent stage, there is chosen a certain number ofpoints PTi, PRi. These points are chosen in limited numbers and aresituated in characteristic zones of universal set M, of image I and ofvirtual reference R. A bijection is then established between the pointsPTi of the image and the points PRi of the virtual reference. Thus, toeach chosen point PTi there is made to correspond a corresponding pointPRi, and vice versa.

For an image, it is possible to obtain a measured field with which itwill be possible to produce measured formatted information.

FIG. 4 a illustrates a possible form of obtaining a measured field. Thisfigure shows universal set M, reference surface SR and medium SC. ImageI is constructed on medium SC by means of an appliance APP3. Then thebijection described in the foregoing is applied. A mathematicalprojection H, preferably a bilinear transformation, is then establishedbetween a point of medium SC and a point of reference surface SR.

In FIG. 4 b it is seen that, for each point PRj of the referencesurface, there can be obtained a point H(PRj) of the image bymathematical projection. Preferably, for two points PRj and PTj of apair associated by bijection, there will be a point H(PRj), themathematical projection of PRj onto medium SC.

A measured field therefore contains:

-   -   for different reference points PR, the mathematical projection        H(PRj) of the reference point PRj onto medium SC, thus providing        a new point H(PRj) associated with the corresponding point PTj        by bijection. Thus, in the measured field, there exists a series        of pairs of points associated by bijection, wherein one point in        each pair is the mathematical projection of the other point of        the pair.

It will also be possible for the measured field of an image to becomposed of any other type of association that links the points PR, PT,H(PR) and H(PT).

It is possible but not necessary to choose variable characteristics ofthe appliance APP3 (or of the appliance chain) among those used toobtain image I with appliance APP3. The variable characteristics of anappliance or of an appliance chain can include the focal length of theoptical system of an appliance, the focus, the aperture, the number ofthe photo in a set of photos, the digital zoom, and the characteristicsof partial capture of an image (“crop” in English terminology), etc.

With this measured field for image I, there is composed a set ofmeasured formatted information IFM. An item of measured formattedinformation of a point PTj will therefore include, according to theforegoing example:

-   -   the fixed characteristics of the appliance or appliances being        used;    -   the chosen variable characteristics;    -   the X, Y position of point PTj in the image;    -   the mathematical projection of the corresponding point PRj by        bijection.

Parameterizable Model

The use of the system will lead to the need to process a large number ofpoints and thus a large volume of measured formatted information. Tomake operation of the system more flexible, to accelerate processingand/or to be resistant to measurement errors, the method provides fordeducing, from items of measured formatted information IFMl to IFMm,items of extended formatted information IFEl to IFEm belonging to asurface (or a hypersurface) that can be represented by a function chosenwithin a space of finite dimension, such as a polynomial of limitedorder chosen among the class of polynomials of finite degree, or aspline function of appropriate degree, or any other approximationfunction.

In the foregoing, it has been seen that formatted information couldcontain variable characteristics. In fact, a combination of variablecharacteristics, such as a combination of focal length, focusing,diaphragm aperture, capture speed, aperture, etc., may be involved.

Under these conditions, the system will be able, during processing of animage, to use, instead of resorting to a large volume of measured and/orextended formatted information, a parameterizable interpolation and/orextrapolation model estimated from measured and/or extended formattedinformation for arguments composed of combinations of known variablecharacteristics.

Arbitrary Point

For an arbitrary point, it is sufficient, for example, to reinject theargument (X, Y, focal length, distance, aperture, iso, speed, flash,etc.) related to this point into the parameterizable model in order tofind the formatted information related to the said point X, Y, and byvirtue of this fact to return to the case of an appliance withoutvariable parameter. By means of the formatted information related to thesaid argument, it is possible to determine, for example, the pointhomologous with X, Y and to suppress all or part of the defect.

Bilinear Transformation

An effective way of calculating the mathematical projection betweenreference surface SR and medium surface SC may be achieved, for example,by choosing, on medium SC and on reference surface SR, four points PTm1to PTm4 and PRm1 to PRm4 that correspond by bijection and that, forexample, are at the peripheral limits of medium SC and of referencesurface SR. The positions of these points are chosen, for example, insuch a way as to maximize the areas included between these points.

In addition, as illustrated in FIG. 5, the positions of these points aresuch that the intersection of the diagonals of the quadrilateralsdefined by these points is located at the center or close to the centerof the quadrilaterals.

There is then calculated a mathematical projection, especially abilinear transformation, for example, with which the four characteristicpoints PTm.1 to PTm.4 can be transformed to the four reference pointsPRm.1 to PRm.4. This mathematical projection will be associated with theformatted information of the image.

Color Images

Referring to FIGS. 6 a to 6 d, a description will be given of methodsfor calculating formatted information related to color images. A colorimage can be regarded as being composed of a plurality of monochromaticimages, each corresponding to one color plane of the color image.Traditionally, it can be considered that a color image is a trichromaticimage composed of three monochromatic images (red, green, blue). It isknown in optics that the distortions induced by the optical systems andthe light-transmission media induce different effects on the differentwavelengths. In a trichromatic image, the same physical defect of anappliance will therefore induce different distortions on the image beingtransported by light of wavelength close to red, on that beingtransported by light of wavelength close to green, and on that beingtransported by light of wavelength close to blue.

As illustrated in FIG. 6 a, starting from a trichromatic universal setM, to which there corresponds a quasi-identical virtual reference R,there will correspond, in image I, three superposed images IR, IG andIB, which have been illustrated separately on the planes SCR, SCG andSCB. The three images IR, IG and IB exhibit different distortions,leading to a trichromatic image that exhibits both geometric distortionand chromatic aberrations.

FIG. 6 b illustrates the principle of the method and system with whichthere can be obtained formatted information that will permitimage-processing software to correct distortions and/or chromaticaberrations.

According to this method, one item of formatted information per colorwill be calculated for each trichromatic point of the image. It willtherefore be considered that it is appropriate to correct as manymonochromatic images as there are colors. In the trichromatic example,the calculations will be performed as if there were three images to becorrected.

For calculation of the formatted information of the three images IR, IGand IB, there are used the same methods as those described in relationto FIGS. 3 to 5.

FIG. 6 b illustrates surface SR with a virtual reference R containingtrichromatic points PR(RGB) and also illustrates the decomposition ofimage I into three monochromatic images IR, IG, IB, each containing thepoints PTR, PTG, PTB of a single color.

One way of calculating the formatted information related to atrichromatic point is to use the same virtual reference R for the threecolor planes. Thus three mathematical projections are used: amathematical projection HR for red point PTR, a mathematical projectionHG for green point PTG and a mathematical projection HB for blue pointPTB, as illustrated in FIG. 6 b.

As shown in FIG. 6 c, another approach is to use the same virtualreference R and to calculate formatted information for each color planeby using the same mathematical projection, defined optionally, onto oneof the color planes. For example, only the mathematical projection HRrelated to the red point is calculated. This mathematical transformationis then applied to the three red, green and blue points to calculate theformatted information of these three points. In this case, it will bepossible for image-processing software to correct both the geometricdistortions and the chromatic aberrations of the image. The combinationof corrected color planes is achieved by simple superposition, sincevirtual reference R and mathematical projection HR are common to thecolor planes.

Another approach, illustrated by FIG. 6 d, comprises:

-   -   For the image of a specified color, such as the red image IR,        calculating the formatted information by using a virtual        reference R assumed to be perfect and a mathematical projection        H(R) of the points of the virtual reference onto the surface of        the red image IR, thus making it possible to correct the        distortions of the red image.    -   For the images of the other colors, such as the green and blue        images IG and IB, using the foregoing color image—the red image        IR according to the adopted example—as virtual reference R′ and        undertaking the same mathematical projection H(IRd) of the        points of this red image onto the surfaces of the green image IG        and then blue image IB. Preferably, this mathematical projection        will be an identity (or identity projection) of the points of        the red image onto the green and blue images. In this way it        will be possible to suppress the differences (chromatic        aberrations) between the red, green and blue images. The        formatted information of the points of the green and blue images        will be able to contain the mathematical projection of the        points of virtual reference R onto the red image as well as the        mathematical projections (identity) of the red image onto the        green and blue images respectively. This approach may make it        possible, as the case may be, to correct the chromatic        aberrations alone by using only the formatted information        related to the green and blue images. The combination of        corrected color planes is achieved by simple superposition,        since virtual reference R and mathematical projection HR are        common to the color planes.

In the foregoing, it was considered that virtual reference R wasquasi-identical to universal set M. If it is considered that virtualreference R is exactly identical to universal set M, it will be possibleto calculate formatted information that will make it possible to correctimage I so that it is the exact replica of universal set M.

As illustrated in FIG. 7, it may be provided that virtual reference R isdeformed compared with universal set M. For example, the virtualreference has a trapezoidal shape, whereas universal set M has arectangular shape. The formatted information that will be obtained willmake it possible to correct image I to induce a trapezoidal deformationon the corrected image. An example of application of such an arrangementexists in overhead projectors, where it will be possible to correct thewell-known deformation induced by these appliances during projectionbecause of the fact that the axis of the projection beam is notperpendicular to the plane of the screen.

It is also possible to deform the virtual reference by distortions, toinduce characteristics and even defects obtained with appliances otherthan those obtained by the appliances with which construction of image Iwas possible. As an example, it will be possible to induce, in thevirtual reference, characteristics of improved appliances oralternatively of old appliances, to impart a particular appearance tothe corrected image. The formatted information, the measured formattedinformation or the extended measured formatted information obtained withsuch a virtual reference incorporate the distortions that were inducedin the virtual reference, in such a way that the formatted informationand/or the measured formatted information can be used by software forprocessing images captured by a first image-capture appliance to obtainimages whose quality, in terms of distortions and/or chromaticaberrations, is comparable to that of a second image-capture appliance.This technique is also applicable to image restitution, by consideringthat image-processing software can then restitute, by means of a firstrestitution appliance, an image whose quality, in terms of distortionsand/or chromatic aberrations, is comparable to that provided by a secondrestitution appliance.

In the foregoing description, it was considered that the image iscomposed of points and that the processing operations of the describedmethods are applied to points. Without departing from the scope of theinvention, however, the described methods could process sets of pointsforming elements and representing patterns (lozenges, etc.).

In the case in which the appliance or the appliance chain possesses avariable characteristic that may have only a reduced number of discretevalues (three discrete values of focal length, for example), it will beof interest, in terms of precision, to employ, according to the adoptedexample, the process with fixed focal length three times rather than touse a polynomial surface corresponding to an approximation that couldinclude the focal length as parameter.

The field of application of the device can cover the field ofapplication related to image quality, its being understood that thequality of images can be measured in terms, among other factors, of theresidual distortion and/or chromatic aberrations that they contain. Theinvention is also applicable to the art of measurement based on visionby computer, known by the expression “vision metrology”.

If the method is employed in the case of an appliance chain containing aplurality of appliances, such as a projector and a photo appliance, orsuch as a printer and a scanner, and if one of the appliances, forexample the photo appliance or the scanner, exhibits zero or littledistortion defect and/or chromatic aberration, the method producesformatted information related solely to the other appliance. This is thecase of a practical method for producing formatted information relatedto an image-restitution appliance by using an image-capture appliancewhich is free of defects or whose defects have been measured andcorrected beforehand.

If the method is employed in the case of an appliance chain containing aplurality of appliances, such as a photo appliance and a scanner, themethod produces formatted information related to both appliances. Thisis the case of a practical method for permitting the correction ofdefects of a photo appliance without having to know the defects of thescanner, in the case in which the images used by the present method andby the image-processing means were scanned with the same appliance.

For the correction proper of an arbitrary image derived from theappliance chain described in the foregoing, a simple example ofimplementation can be described as follows:

-   -   Reading of the formatted information related to the appliance        chain and calculated beforehand. This formatted information        contains in particular the parameterizable model described in        the foregoing.    -   Reading of all the information of the format style—Exif, PIM or        other—giving particulars about the set of adjustments of the        appliance and/or of the appliance chain at the moment of filming        (focal length, focusing, aperture, speed, flash, etc.). This        information comprises values of variable parameters of the        device and a part of the arguments of the parameterizable model.        This information is generally indicated, for example, in the        image headers.    -   Correction: For each point having coordinates (X,Y) on SR and        corresponding to a point of the corrected image to be        calculated, it is possible to compose a complete argument of the        parameterizable model with the coordinates X,Y and the foregoing        part of the arguments of the parameterizable model: (X, Y, focal        length, distance, aperture, iso, speed, flash, etc.). It is then        possible, by virtue of the formatted information, to calculate        the coordinates of a point (X′,Y′) of the image to be corrected.        The values of (X′,Y′) will not necessary be integral. The        brightness associated with the point is then calculated by        applying, for example, any interpolation technique (linear,        bilinear, bicubic or other) to the brightness information taken        at the point (X′Y′) and its vicinity in the image to be        corrected. This method is iterated for all the points of the        image and for each color plane, in such a way as to obtain a        defect-free image.

The system in FIG. 8 represents a form of employment of the inventiondescribed in the foregoing. A digitized color image plane 4 is processedby a first calculating means 16, which models and corrects the geometricanomalies of the said digitized color planes 4, in such a way as toobtain corrected digitized color planes 17. A second calculating means18 combines the said corrected digitized color planes 17, in such a wayas to obtain a color image 19 corrected completely or partly for thechromatic aberrations 1.

Calculation means 16 may also model and correct, at least partly, thesaid geometric anomalies composed of deviations 10, especiallydistortion, between the geometric defects 2, of the said digitized colorplanes 4, in such a way as to obtain corrected digitized color planes17.

The system in FIG. 9 represents another form of employment of theinvention described in the foregoing. Calculating means 6 are able tomodel and correct, at least partly, the geometric anomalies composed ofdistortion defects 2 of the said digitized color planes 4, in such a wayas to obtain corrected digitized color planes 7, so that it is possibleestablish a correspondence between the said corrected digitized colorplanes 7.

Second calculating means 8 illustrated in FIG. 9 then make it possible,by combining the said corrected digitized color planes 7, to obtain acolor image 9 corrected completely or partly for the chromaticaberrations 1 and/or the distortion defects 2.

1. A method for correcting chromatic aberrations of a color imagecomposed of a plurality of digitized color planes, the color imagehaving been produced by means of an optical system, the methodcomprising: modeling and correcting, at least partly, the geometricanomalies composed of deviations between geometric defects of thedigitized color planes, to obtain corrected digitized color planes,wherein it is possible to establish a correspondence between thecorrected digitized color planes; and combining the corrected digitizedcolor planes to obtain a color image corrected completely or partly forthe chromatic aberrations, wherein the step of modeling and correctingfurther comprises: producing, by means of an appliance or an appliancechain, an image of a reference scene, the image exhibiting defects,producing, from the reference scene, a virtual reference, establishing abijection between the image and the virtual reference, calculatingprojections of the virtual reference onto three digitized color planesR, G and B, using a same mathematical projection for each of the threedigitized color planes, calculating formatted information comprisingmathematical projections, and correcting the chromatic aberrations ofthe image based on the formatted information.
 2. A method for correctingthe distortion defects of a color image composed of a plurality ofdigitized color planes, the color image having been produced by means ofan optical system and configured to correct distortion defects of thecolor image, the method comprising: modeling and correcting, at leastpartly, the geometric anomalies composed of distortion defects of thedigitized color planes, to obtain corrected digitized color planes,wherein it is possible to establish a correspondence between thecorrected digitized color planes; and combining the corrected digitizedcolor planes to obtain a color image corrected completely or partly thedistortion defects, wherein the step of modeling and correcting furthercomprises: producing, by means of an appliance or an appliance chain, animage of a reference scene, the image exhibiting defects, producing,from the reference scene, a virtual reference, establishing a bijectionbetween the image and the virtual reference, calculating projections ofthe virtual reference onto three digitized color planes R, G and B,using a same mathematical projection for each of the three digitizedcolor planes, calculating formatted information comprising mathematicalprojections, and correcting the distortion defects of the image based onthe formatted information.
 3. A system for correcting chromaticaberrations of a color image composed of a plurality of digitized colorplanes, the color image having been produced by an optical system; thesystem comprising: first calculating means for modeling and correctinggeometric anomalies of the digitized color planes, to obtain correcteddigitized color planes; and second calculation means for combining thecorrected digitized color planes, to obtain a color image correctedcompletely or partly for the chromatic aberrations, wherein the firstcalculating means for modeling and correcting geometric anomaliesfurther comprises: first producing means for producing, by means of anappliance or an appliance chain, an image of a reference scene, theimage exhibiting defects, second producing means for producing, from thereference scene, a virtual reference, establishing means forestablishing a bijection between the image and the virtual reference,third calculating means for calculating projections of the virtualreference onto three digitized color planes R, G and B, using a samemathematical projection for each of the three digitized color planes,fourth calculating means for calculating formatted informationcomprising mathematical projections, and correcting means for correctingthe distortion defects of the image based on the formatted information.4. A system according to claim 3, wherein: the first calculating meansfurther for modeling and correcting, at least partly, the geometricanomalies composed of deviations between geometric defects of thedigitized color planes to obtain corrected digitized color planes,wherein it is possible to establish a correspondence between thecorrected digitized color planes; and the second calculating meansfurther for combining the corrected digitized color planes to obtain acolor image corrected completely or partly for the chromaticaberrations.
 5. A system according to claim 3, configured to correctchromatic aberrations and distortion defects of the color image, thesystem further comprising: first calculating means further for modelingand correcting, at least partly, the geometric anomalies composed ofdistortion defects of the digitized color planes to obtain correcteddigitized color planes, wherein it is possible to establish acorrespondence between the corrected digitized color planes; and secondcalculating means further for combining the corrected digitized colorplanes to obtain a color image corrected completely or partly for thechromatic aberrations and the distortion defects.